A Permutation Test for Unbalanced Paired Comparisons of Global Field Power

Global field power is a valuable summary of multi-channel electroencephalography data. However, global field power is biased by the noise typical of electroencephalography experiments, so comparisons of global field power on data with unequal noise are invalid. Here, we demonstrate the relationship between the number of trials that contribute to a global field power measure and the expected value of that global field power measure. We also introduce a statistical testing procedure that can be used for multi-subject, repeated-measures (also called within-subjects) comparisons of global field power when the number of trials per condition is unequal across conditions. Simulations demonstrate the effect of unequal trial numbers on global field power comparisons and show the validity of the proposed test in contrast to conventional approaches. Finally, the proposed test and two alternative tests are applied to data collected in a rapid serial visual presentation target detection experiment. The results show that the proposed test finds global field power differences in the classical P3 range; the other tests find differences in that range but also at other times including at times before stimulus onset. These results are interpreted as showing that the proposed test is valid and sensitive to real within-subject differences in global field power in multi-subject unbalanced data.